Registered: Mar 2005
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Recently I mentioned in one of the threads that there exists a proof that there can be no "perfect" voting system. In the science of voting methods, this is measured by testing a particular system to see which criteria it passes or fails.

One of the most well-accepted, and seemingly obvious, criteria for a good voting system to comply with is called "independence of irrelevant alternatives", meaning that if candidate A is preferred to candidate B in the race, and then a third candidate, C, is introduced, then either A should still win, or C should win. But it would make no sense if adding C caused B to defeat A, if the voters' preferences hadn't changed. What Arrow's theorem famously proves, is that there exist scenarios in which no voting system, not just one you can think of, can pass this test. For example, say you have the following breakdown of 100 voters, the first line specifying that 65 people prefer A over B over C:

40 A > B > C
35 B > C > A
25 C > A > B

There may be an infinite number of voting systems, but ultimately a voting system must choose one of the three as the winner. So say the system chooses A. Now, had B dropped out of the race, 60% of the delegates would prefer C to A, and so any reasonable voting system would have to say that C should actually have been the winner.

So let us say that the voting system chooses B as the winner. Now, if C were to drop out, A would beat B 65 to 35.

Say the system chooses C as the winner. If A were to drop out, 75% of the people would prefer B to C.

This is but one type of criteria that no voting system can be completely impervious to. Some criteria are met by some voting systems, but not by others.

Arguably, our current "largest as first choice" system, in the U.S., is the worst. Consider the following scenario:

35% BUSH > GORE > NADER
34% GORE > NADER > BUSH
31% NADER > GORE > BUSH

In our current system, Bush would win (especially if he cheated!), yet Gore and Nader are preferred to Bush by 65% of the people. In the real world, the latter group would employ tactical voting--lie and say that they wanted Gore instead of Nader, so that they wouldn't get Bush. Trying to reduce the incentive for the voter to insincerely rank his preferences is another ideal of the "perfect voting system".

This is a problem that is solved by Condorcet voting methods, which essentially rank every pair of candidates against each other and produce the person who is defeated by no one else in a head-to-head race (if there is one). Occasionally this produces a situation where A > B > C > A > B > C , etc., and this is called a circular ambiguity. The method used to resolve a circular ambiguity, should one exist, is what differentiates the various Condorcet methods. The Condorcet method that i think is the best is called the Schulze method.

While there exist a number of voting methods, a few general groups stand out. There is the current "majority" method, which I think I hear people refer to as "first past the post"?). There is range voting, of which approval voting is a subset. There is Borda, in which candidates are given points depending on their rank. And then there are the Condorcet methods. Wikipedia has some pretty decent background on them.

My contention is that Schulze, and Condorcet in general, is by far the best, by I'd like to test that and see what other perspectives people have.

Last edited by BROKEN_LADDER on 07-11-2006 at 02:22 AM

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cheated cheated cheated....

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An interesting fact: The poll I posted only allows for us to calculate the winning answer via "first past the post"...or if I had chosen to allow multiple answers, then approval voting. Maybe we should first have a vote on which is the right method to use to choose the winner. But first we'll have to decide what voting system to use when we take that vote. So let's have a vote about that. But...wait...

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god dammit people! this matters!

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Registered: Apr 2005
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This thread makes me want pizza.

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quote:

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Originally posted by fubar
This thread makes me want pizza.

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I have voted in every election since I turned 14.

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We do vote. We just don't vote for people that are guaranteed to lose like you do.

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quote:

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Originally posted by Trenchant_Troll
We do vote. We just don't vote for people that are guaranteed to lose like you do.

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Okay, get this. I'm debating with this professor right now, Warren D. Smith, who advocates range voting, and in particular one very odd ramification of range voting. That a majority vote could be overruled by the zealousness of the minority. Here's an example.

51% of the people have Gore as their first choice, and like Bush just a little bit less. (obviously this is hypothetical)
49% of people love Bush, and hate Gore.

He says Gore should win.

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Just so that this is recorded out in cyberspace, I want to let the world know, I've devised the best possible voting method--I'm sure of it. I will call it the Schentrup method, in honor of myself. Here's how it works.

You start out by voting as in range voting. You give a number within the specified range to each candidate (any that you don't care about automatically get a 0). A reasonable range would be 0-99, although you can multiply this by a factor of 10 to provide higher resolution (or just use something like 65.5 if you feel like it). The point is that if there are two people you like about equally, you should still indicate preference if there is any, even by using just a single point. Now this part is just regular range voting. But here's where things change in the Shentrup method.

Instead of adding up all the votes, like you normally do, you use each voter's weightings to glean his preferred ordering, and then treat it like a traditional Condorcet vote. Only if there is a circular ambiguity do you fall back to using range voting, eliminating every candidate who doesn't lie within the Smith set.

As far as I can tell, this eliminates all incentive for tactical voting.

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Okay, this professor dude I'm debating with, who advocates range voting, and has taught at Princeton...and is a fucking bad ass, proved to me that the previous method I proposed allowed for cases of the no show paradox, where the candidate you want to win would win...unless you showed up and voted for him. Rare, but possible. Arggh!! Voting is insanely complicated. It could be an entire course, like calculus or statistics. Anyway, from my latest email to him, here's my latest proposed method:

The only candidate who could be selected without allowing for the possibility of a no show paradox is B. In your PDF scenario, B was the only candidate who couldn't be selected. Anyway...somehow the idea that a candidate wins the ambiguity resolution solely because we have to prevent a no show paradox seems...bizarre.

Anyway, I think I've found an end to the whole bloody mess. I've always felt intuitively that Condorcet was a paramount criterion, but I wanted a way to solve a CA in such a way as to model what infinitely stubborn, omniscient (as to the preferences of all other voters) voters would decide in arbitration. But then I just realized...or re-realized...that in any real circular ambiguity, there's no reason for an infinitely stubborn person to give in and help someone else get first place so that he can get second instead of last preference. He might as well hold out until someone else gives in and helps him get first place. Of course, assuming all voters act the same way (which ideally they should), they arbitrate forever.

So the solution requires a coin toss. You have everyone do a range vote, and use it ordinally, to do Condorcet. In the case of an ambiguity you remove everyone's scores for candidates other than those in the Smith set, and re-scale them. Then you pick one of those candidates in the Smith them at random, such that any candidate's probability of of being picked is equal to his score, divided by the sum of the scores of all candidates in the Smith set.

Thoughts?

In admiration of your super genius,
Clay

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quote:

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Originally posted by BROKEN_LADDER
Why not? How does a platform ever build the momentum it needs to eventually become a serious contender if people don't start voting?

And as we've discussed in the forum before, voting for a third party shows the other parties that they are losing out because people hate them so much that they're willing to "waste" a vote for a "third party". in that sense, i'd say voting for the libertarian party makes perfect sense.

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Registered: Apr 2005
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I have a better voting method.

Take all the candidates and connect them to each other with a 20 foot long piece of bungie cord. Tie their arms behind their backs, and wrap both legs together at the knees. In their mouths, place a ball gag with a 4 inch blade sticking out of it. Put them in a room with all the lights out and and tell them "there can be only one".

Televise it (IR cameras), of course, because one does want to be abreast of domestic politics.

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Warren,

I've got it! The solution is for delegate/group 3 to pick C with a probability of 1. Then, in line with this, delegate 2 should pick candidate B with probability 1, and what delegate 1 (who prefers candidate A) does, is really inconsequential, unfortunately for him; although he should put 100% probability into candidate A. The reasoning for this seems simple now that I've come across it.

For delegate/group 1, there is no reason to put any investment in voting for B, as this is only as helpful as the probability that delegate 2 has for picking B, and in the case that he does pick B, delegate 1 would have been better served choosing candidate A, since he has the same odds of that choice's "winning" either way, except he values candidate A more, giving him a higher expected value for doing that.

For delegate 2, any probability he donates toward choosing candidate B just serves to increase the likelihood of a 3-way split, electing candidate A, which has zero value to him anyway. It would be great for delegate 1 if he could "promise" to delegate 2 that he'd actually put some probability into candidate B, but again, if doing that gave him any probability that deleget 2 would actually put probability into candidate B, he'd want to use that by putting all of his probability into candidate A anyway. It's a bizarre effect; the fact that even if he promises to do this it would be better for him not to, stops delegate 2 from having any reason to take his word.

Finally, for delegate 3, if delegate 2 were to put any probability into candidate B (or say all 100% of it), then of course delegate 1 would have all reason to put all his eggs in the candidate A basket, meaning that his probability donated toward candidate C would have as much strength toward electing candidate A as it would if he put that probability into candidate A directly; plus it would have the added benefit of helping his first-preferred candidate C. So again, it makes sense for him to put 100% of his probability into candidate C.

What this means is that my theory, that a Nash equilibrium for this 3-way situation might actually be such that there'd be no incentive to misrepresent, turns out to be false. Counterintuitively, it actually helps the least preferred candidate, mainly because he has "nothing to lose"--a very strange consequence of that fact. Both candidate A and B could potentially win with a 3-way split (in the latter case, delegate 1 would pick his second favorite, candidate B). This is basically a consequence for delegate 1 that he has the benefit of being able to win with a split. Because he has the incentive to do that, it keeps him appearing "dishonest" to delegate 2, such that delegate 2 has no reason to invest any probability in candidate B.

I'm now frustrated that I spent so much time racking my brain over this apparently simple result. However, one thing it reminds me of is my belief there there is always a "Nash equilibrium", no matter how many ways you split the situation (in this case, three groups), because there's always a "best strategy". In this case that turned out to be true; if you set it up as I've described here, no delegate can do better by changing his probability for picking a certain candidate, while the other delegates' choices remain fixed.

But now to tie this back into the resolution of Condorcet ambiguities. In this scenario, I have "simplified" the situation by substituting individual delegates for groups with similar preferences. This can be likened to groups where all members have identical preferences and thus goals, and all vote identically, in a sort of uncommunicated collusion. What's strange about the result, as I mentioned, is that delegate (or "group") 1 actually loses out because he has more power to win, or simply put, more ways to win. But why is this? Going back to the original scenario, it was because one delegate had to represent the group that was most populous (that's oversimplifying, and it depends on which Condorcet resolution algorithm we use, but you know what I mean). What this means then is that it would actually be beneficial for the group if enough individuals within it were to misrepresent, such that a split wouldn't help delegate 1 in this example, and group 2 would have a reason to give some of its probability to candidate B (because delegate 1 wouldn't benefit from a split, and would therefore do the same). So there you have it: a scenario in which a delegate group wants to have less power so that it can ultimately have more power. If you are in the Schwarz set, it pays to have your first choice be the ambiguity-resolution-winner's last choice, so that you can force a mass lie, which produces a fake Condorcet winner and negates the ambiguity in the first place.

Does this "hot potato" effect (or maybe "hot medal" effect) ultimately mean that with an omniscient electorate under Condorcet, all delegates who will end up with their Candidates in the Schwarz set should actually act to give their favored candidate the worst results that still get him into the Schwarz set? If so, does this mean about the ultimate honesty of a perfectly strategic electorate in a Condorcet system?

Clay

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quote:

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Originally posted by BROKEN_LADDER
god dammit people! this matters!

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Probably to every person who votes, if he really thinks about it. What's the point of voting, if the voting system is inherently flawed?

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Sounds to me as if you're advocating that only reasonably intelligent people vote, since the methods you desribe would confound most of Bush's supporters.

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You don't have to understand the math behind the voting method to simply use it.

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People get confused by simple paper ballots using the existing system.
Even less than intelligent people would want to have some idea of whom they might be electing and they won't if they don't understand the process.

I work as an election official and around 40% of the time I have to explain how the voting machine they used a year or two ago works.

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